Neuron calculator for artificial neural networks

ABSTRACT

Examples described herein include systems and methods, including wireless devices and systems with neuron calculators that may perform one or more functionalities of a wireless transceiver. The neuron calculator calculates output signals that may be implemented, for example, using accumulation units that sum the multiplicative processing results of ordered sets from ordered neurons with connection weights for each connection between an ordered neuron and outputs of the neuron calculator. The ordered sets may be a combination of some input signals, with the number of signals determined by an order of the neuron. Accordingly, a k th -order neuron may include an ordered set comprising product values of k input signals, where the input signals are selected from a set of k-combinations with repetition. As an example in a wireless transceiver, the neuron calculator may perform channel estimation as a channel estimation processing component of the receiver portion of a wireless transceiver.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.16/115,866 filed Aug. 29, 2018 and issued as U.S. Pat. No. 10,601,471 onMar. 24, 2020. The aforementioned application, and issued patent, isincorporated herein by reference, in its entirety, for any purpose.

BACKGROUND

Artificial neural networks are used in many applications, includingimage and speech recognition. Fifth generation (5G) wirelesscommunication systems, including those employing multiple-inputmultiple-output (MIMO) techniques or “massive MIMO” techniques, in whichmultiple antennas (more than a certain number, such as 8 in the case ofexample MIMO systems) are utilized for transmission and/or receipt ofwireless communication signals, also have applications for artificialneural networks. However, in increasing the learning of neural networks,the number of neurons and corresponding weights of the neural networkmay increase exponentially, overwhelming the memory and power limits ofdevices implementing such schemes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic illustration of an example system arranged inaccordance with examples described herein.

FIG. 1B is a schematic illustration of an example processing unitarranged in accordance with examples described herein.

FIG. 2 is a schematic illustration of a system arranged in accordancewith examples described herein.

FIG. 3 is a schematic illustration of a wireless transmitter.

FIG. 4 is a schematic illustration of wireless receiver.

FIG. 5 is a schematic illustration of an electronic device arranged inaccordance with examples described herein.

FIG. 6 is a schematic illustration of a neuron calculation method inaccordance with examples described herein.

FIG. 7 is a schematic illustration of a wireless communications systemarranged in accordance with aspects of the present disclosure.

FIG. 8 is a schematic illustration of a wireless communications systemarranged in accordance with aspects of the present disclosure.

FIG. 9 is a block diagram of a computing device arranged in accordancewith examples described herein.

DETAILED DESCRIPTION

Neural networks continue to be utilized in various memory-intensive andpower-intensive applications, such as image recognition, wirelesscommunication and speech recognition. Due in part to such memory andpower demands, processor implementations may become more costly asneural networks grow larger. For example, the numbers of the weightsand/or dimensions of weight matrices that are used to connect neuronsmay increase exponentially as the number of layers of neural networksincreases and/or additional neurons are added to a network. To meetthese demands, in some neural network applications, weights may becompressed and/or pruned to reduce the number of weights and/or neurons.However, because an additional, often onerous, process may be employedto identify and determine which weights to reduce, such pruning orcompression of neural networks may often not be implemented withoutintroducing additional complexity to the neural network, such asincreased power or memory consumption. For example, weights inconventional schemes may be determined using a least-mean squaresalgorithm to produce weights with a large precision value, which mayundesirably utilize additional memory.

Examples described herein may calculate and provide ordered sets forneural networks that utilize input signals as the basis for the orderedsets, thereby forming a neural network that utilizes less memory, orthat uses memory more efficiently, than conventional schemes. Incontrast to examples of conventional neural network arrangements thatmay store weights/parameters unrelated to the input signals, the systemsand methods described herein may utilize input signals which may alreadybe allocated memory storage as the basis for computing weights and/orelements of the neural network.

By associating neurons in a neural network with certain combinations ofthe input signals, the number of elements may be finite, therebyfacilitating memory allocation. An additional advantage of such memoryallocation includes increasing processed speed (e.g., by utilizingalready known input signals); in contrast to conventional neuralnetworks that may decrease processing speed, while attempting toincrease a precision of a given neural network. For example, inaccordance with examples of methods and systems described herein, aneuron calculator may calculate ordered sets based on the input signalsand an order of a respective neuron to provide ordered sets forutilization as a neural network. The ordered sets may be amultiplicative combination of a number of the input signals, with thenumber of signals determined by an order of the neuron. Accordingly, ak^(th)-order neuron may include an ordered set including product valuesof k input signals, where the input signals are selected from a set ofk-combinations with repetition.

FIG. 1A is a schematic illustration of an example neural network 10arranged in accordance with examples described herein. The neuralnetwork 10 includes a memory 15 and a neuron calculator 18 with inputs20, 22, and 28 for input signals x₁(n), x₂(n), x_(k)(n) respectively andoutputs 40, 42, and 48 for output signals z₁(n), z₂(n), z_(l)(n). Theneuron calculator 18 also includes ordered neurons, such as afirst-order neuron 30, a second-order neuron 32, and a k'th order neuron38. The neuron calculator 18 calculates the ordered sets, utilized atthe respective ordered neurons 30, 32, and 38, based on the inputsignals x₁(n), x₂(n), x_(k)(n). Once calculated, the ordered sets may bestored in memory 15 for further input signals (e.g., additional inputsignals received at 20, 22, and 28) to adjust and/or compensate suchfurther input signals for an error in the further input signals (e.g., awireless channel error of a wireless channel). In such an example, theinput signals x₁(n), x₂(n), x_(k)(n) may correspond to inputs forrespective antennas of transceivers receiving the respective inputsignals x₁(n), x₂(n), x_(k)(n); while the output signals z₁(n), z₂(n),z_(l)(n) may correspond to compensated signals with a reduced channelestimation error, as compared to the input signals x₁(n), x₂(n),x_(k)(n).

As described herein, the ordered sets stored in memory 15 to beimplemented in respective ordered neurons 30, 32, and 38 may be amultiplicative combination of a number of the input signals, with thenumber of signals determined by an order of the neuron. Accordingly, forthe first-order neuron 30, the first-ordered set comprises p_(i)elements, where N₁ is the number of input signals:p _(i) ⁽¹⁾(n)=x _(i)(n) (i=1,2, . . . ,N ₁)As denoted herein, the ⁽¹⁾ superscript of a p_(i) element denotes theorder of that element in that ordered set. Accordingly, the ⁽¹⁾superscript indicates a first-order. For the second-order neuron 32, thesecond-ordered set comprises p_(ij) elements, where N_(i) ⁽²⁾ and N_(j)⁽²⁾ are the number of input signals.p _(ij) ⁽²⁾(n)=x _(i)(n)x _(j)(n) (i=1,2, . . . , N _(i) ⁽²⁾ j=1,2, . .. ,N _(j) ⁽²⁾)Because the ordered sets are sets of k-combinations with repetition, thetotal number of the i and j input signals are the same; resulting in amaximum number of second-order elements being N_(i) ⁽²⁾×N_(j) ⁽²⁾, whichequals N²p_(ij) elements of the second-ordered set to be utilized in thesecond-order neuron 32. As an example, the neuron calculator 18 maycalculate a second-ordered set for three input signals x₁(n), x₂(n),x₃(n) to be p_(ij) elements, as shown in Table 1.

TABLE 1 x₁(n) x₂(n) x₃(n) x₁(n) p₁₁ ⁽²⁾(n) = x₁ ²(n) p₁₂ ⁽²⁾(n) =x₁(n)x₂(n) p₁₃ ⁽²⁾(n) = x₁(n)x₃(n) x₂(n) p₂₁ ⁽²⁾(n) = x₂(n)x₁(n) p₂₂⁽²⁾(n) = x₂ ²(n) p₂₃ ⁽²⁾(n) = x₂(n)x₃(n) x₃(n) p₃₁ ⁽²⁾(n) = x₃(n)x₁(n)p₃₂ ⁽²⁾(n) = x₃(n)x₂(n) p₃₃ ⁽²⁾(n) = x₃ ²(n)In Table 1, six independent elements represent the second-orderelements, and, accordingly, may be utilized as the second-ordered setrepresenting nonlinearities of the second-order for the input signalsx₁(n), x₂(n), x₃(n). Continuing in the example, for the k'th orderneuron 38, the k'th-ordered set comprises p_(i) ₁ _(i) ₂ _(. . . i) _(k)^((k)) elements:p _(i) ₁ _(i) ₂ _(. . . i) _(k) ^((k))(n)=x _(i) ₁ (n)x _(i) ₂ (n) . . .x _(i) _(k) (n)Accordingly, the maximum number of k'th-order elements being N^(k)elements of the k'th-ordered set to be utilized in the k'th-order neuron38. As an example, the neuron calculator 18 may calculate a k'th-orderedset for three input signals x₁(n), x₂(n), x₃(n) to be p_(ijk) elements,as shown in Table 2.

TABLE 2 p₁₁₁ ⁽³⁾(n) = x₁ ³(n) p₂₂₁ ⁽³⁾(n) = x₂ ²(n)x₁(n) p₃₃₁ ⁽³⁾(n) =x₃ ²(n)x₁(n) p₁₁₂ ⁽³⁾(n) = x₁ ²(n)x₂(n) p₂₂₂ ⁽³⁾(n) = x₂ ³(n) p₃₃₂⁽³⁾(n) = x₃ ²(n)x₂(n) p₁₁₃ ⁽³⁾(n) = x₁ ²(n)x₃(n) p₂₂₃ ⁽³⁾(n) = x₂²(n)x₃(n) p₃₃₃ ⁽³⁾(n) = x₃ ³(n) p₁₂₃ ⁽³⁾(n) = x₁(n)x₂(n)x₃(n)In Table 2, ten independent elements represent the third-order elements,and, accordingly, may be utilized as the third-ordered set representingnonlinearities of the third-order for the input signals x₁(n), x₂(n),x₃(n).

Again with reference to FIG. 1A, the inputs 20, 22, and 28 of the neuroncalculator 18 may be implemented, for example, using bit manipulationunits that may forward the input signals x₁(n), x₂(n), x_(k)(n) to theordered neurons 30, 32, and 38. The ordered neurons 30, 32, and 38 maybe implemented, for example, using multiplication units that include arespective ordered set. In some examples, the respective ordered set maybe calculated by neuron calculator 18 in each ordered neuron 30, 32, and38; and stored in the memory 15. The outputs 40, 42, and 48 may beimplemented, for example, using accumulation units that mix (e.g., sum)the respective ordered sets at each of the ordered neurons 30, 32, and38 with connection weights for each connection between an ordered neuron30, 32, and 38 and an output 40, 42, and 48. For example, eachconnection may be weighted with a weight ‘W_(l),’ where l represents thetotal number of weights for the connections. In some examples, ‘W_(l),’may be a matrix. For example, each connection between the ordered neuron30, 32, and 38 and the outputs 40, 42, and 48 are weighted. The neuroncalculator 18 sums the ordered sets and the connection weights at theoutputs 40, 42, and 48 to generate output signals z₁(n), z₂(n),z_(l)(n). In example, summation at each respective output 40, 42, and 48may be represented as:

$\begin{matrix}{{z_{l}(n)} = {q_{l}\left( {{\sum\limits_{i = 1}^{N_{1}}\;{{W_{l}(i)}{p_{i}^{(1)}(n)}}} + {\sum\limits_{i = 1}^{N_{i}^{(2)}}\;{\sum\limits_{j = 1}^{N_{j}^{(2)}}\;{{W_{l}\left( {i,j} \right)}{p_{ij}^{(2)}(n)}}}} + \cdots + {\quad{\sum\limits_{i_{1} = 1}^{N_{i_{1}}^{(k)}}\;{\sum\limits_{i_{2} = 1}^{N_{l_{2}}^{(k)}}{\cdots{\sum_{i_{k} = 1}^{N_{i_{k}}^{(k)}}{{W_{l}\left( {i_{1},{i_{1}\cdots\mspace{11mu} i_{k}}} \right)}{p_{i_{1}i_{2}{\cdots i}_{k}}^{(k)}(n)}}}}}}}} \right.}} & {{Equation}\mspace{14mu} 1}\end{matrix}$In Equation 1, l corresponds to each output of each neuron (e.g.,neurons 30, 32, and 38), q_(l)(⋅) is the activation function of the l'thoutput of each neuron and W_(l)(⋅) is the corresponding connectionweight set between the l'th output and the k'th-ordered neuron. UsingEquation 1, the connection weights can be determined by the neuroncalculator 18. For example, the neuron calculator 18 may utilize aleast-mean squares algorithm to determine connection weights. Forexample, an error, ε, may be minimized between calibration signalsprovided to the neuron calculator 18 and the output signals z₁(n),z₂(n), z_(l)(n). In the context of Equation 2, Z(n) may be a pluralityof calibration signals provided to the neuron calculator 18 at inputs20, 22, and 28, where M denotes how many calibration signals areprovided to the neuron calculator 18.

$\begin{matrix}{\epsilon = {\sum\limits_{n = 1}^{M}\;{{{Z(n)} -}}^{2}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$As an example of applying Equation 2 to determine connection weightswith calibration signals, a gradient descent method may be utilized tooptimize the value of connection weights. For example, connectionweights may be initially randomly selected (e.g., all connection weightsmay equal zero initially). The neuron calculator 18 calculates theoutputs 40, 42, and 48 for the calibration signals in accordance withEquation 1. The neuron calculator 18 calculates the error at each of theoutputs 40, 42, and 48. The calculated error, δ_(l)(n), at each of theoutputs 40, 42, and 48, where ordered sets and the connection weightsare summed, may be represented by Equation 3; with z(n) being thecorresponding output of the neuron calculator 18 (e.g., outputs 40, 42,and 48) of a total number of outputs, L; where v_(l)(n) is the weightedsummation of the l'th neuron of the outputs 40, 42, and 48; and where[q_(l)(v_(l)(n)]′ is the gradient of the l'th neuron of the outputs 40,42, and 48.

$\begin{matrix}{{\delta_{l}(n)} = {{{\left\lbrack {{\hat{z}(n)} - {z(n)}} \right\rbrack\left\lbrack {q_{l}\left( {v_{l}(n)} \right)} \right\rbrack}{\,^{\prime}\left\lbrack {q_{l}\left( {v_{l}(n)} \right)} \right\rbrack^{\prime}}} = {\frac{\partial{q_{l}(u)}}{\partial u}\text{|}_{u = {v_{l}{(n)}}}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$Accordingly, the neuron calculator 18 may compute an individual error ofeach output 40, 42, and 48 after summing the ordered sets and theconnection weights at the outputs 40, 42, and 48 to generate outputsignals z₁(n), z₂(n), z_(l)(n). As an example of the summation forcalculating an error of respective calibration signals, continuing withthe denotation of ordered sets and connection weights of Equation 1, theneuron calculator is configured to mix (e.g., sum) at each respectiveoutput 40, 42, and 48 the ordered sets and connection weights with thecalibration signals Z(n), as expressed in Equation 4.

$\begin{matrix}{{v_{l}(n)} = {{\sum\limits_{i = 1}^{N_{1}}\;{{W_{l}(i)}{p_{i}^{(i)}(n)}}} + {\sum\limits_{i = 1}^{N_{i}^{(2)}}\;{\sum\limits_{j = 1}^{N_{j}^{(2)}}\;{{W_{l}\left( {i,j} \right)}{p_{ij}^{(2)}(n)}}}} + \cdots + {\underset{i_{1} = 1}{\overset{N_{i_{1}}^{(k)}}{\quad\sum}}\;{\sum\limits_{i_{2} = 1}^{N_{i_{2}}^{(k)}}{\cdots{\sum_{i_{k} = 1}^{N_{i_{k}}^{(k)}}{{W_{l}\left( {i_{1},{i_{1}\cdots\mspace{11mu} i_{k}}} \right)}{p_{i_{1}i_{2}{\cdots i}_{k}}^{(k)}(n)}}}}}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Continuing in the example of determining the connection weights, theinitial connection weights may be updated according to Equation 5.ΔW _(l)(i ₁ ,i ₁ . . . i _(k))=αΣ_(n=1) ^(M)δ_(l)(n)p _(i) ₁ _(i) ₂_(. . . i) _(k) ^((k))(n)  Equation 5For example, the neuron calculator 18 may sum the product of thecalculated error, δ_(l)(n), at each of the outputs 40, 42, and 48, withthe elements of each ordered neuron. In accordance with Equation 5, thatsummation may be multiplied by a learning-rate factor, α. In someexamples, various sets of M calibration signals may be provided to theneuron calculator 18 to continue updating the connection weights. Oncethe weights have converged, in accordance with gradient descent methods,the connection weights may be stored in memory 15 for use by the neuroncalculator 18 to map various inputs signals to output signals. Forexample, the neuron calculator 18 may function as a processing componentof a wireless transceiver. For example, the neuron calculator 18 mayperform channel estimation as a channel estimation processing componentof the receiver portion of a wireless transceiver. Accordingly, in thecontext of a neuron calculator 18 being a channel estimation processingcomponent, the neuron calculator 18 may include ordered sets andconnection weights that, when applied to a wireless input signal, removeor reduce an error introduced by a wireless channel. In variousexamples, a neuron calculator 18 or several neuron calculators mayoperate in conjunction with a wireless transceiver to perform variouswireless processing component functionalities.

The neuron calculator 18 can be implemented using one or more processingunits, for example, having any number of cores. An example processingunit can include an arithmetic logic unit (ALU), a bit manipulationunit, a multiplication unit, an accumulation unit, an adder unit, alook-up table unit, a memory look-up unit, or any combination thereof.For example, a processing unit 58 is described with reference to FIG. 1Bincluding multiplication units, accumulation units, and, memory look-upunits.

In an example processor core, a set of instructions can be loaded thatimplements calculations performed by the neuron calculator 18. In someexamples, the neuron calculator 18 may include circuitry, includingcustom circuitry, and/or firmware for performing functions describedherein. For example, circuitry can include multiplication unit,accumulation units, and/or bit manipulation units for performing thedescribed functions, as described herein. The neuron calculator 18 maybe implemented in any type of processor architecture including but notlimited to a microprocessor or a digital signal processor (DSP), or anycombination thereof. In an example processor core, a set of instructionscan be loaded that implements the training of the neuron calculator 18being provided calibration signals, e.g., training the neuron calculator18 to determine the elements of the ordered sets and the connectionweights.

In FIG. 1A, the neuron calculator 18 has been described with respect toa single layer of ordered neurons 30, 32, and 38, with a layer being anintermediate connection node between the inputs 20, 22, and 28 and theoutputs 40, 42, and 48. For example, each ordered neuron 30, 32, and 38is an individual multiplication unit. It can be appreciated thatadditional layers of ordered neurons with multiplication units may beadded between the inputs 20, 22, and 28 and the outputs 40, 42, and 48.For example—in an embodiment in which additional neurons are includedbetween the inputs 20, 22, and 28 and the ordered neurons 30, 32, and38—the ordered neurons 30, 32, and 38 may represent a last layer ofneuron calculator 18 having several layers of ordered neurons. In such acase, Equation 1 may represent a summation at each respective output 40,42, and 48 of this last layer of the neuron calculator 18. The neuroncalculator 18 may be scalable in hardware form, with additionalmultiplication units being added to accommodate additional layers.

FIG. 1B is a block diagram of a processing unit 58 in a neural network50, which may be implemented as a neuron calculator 18, in accordancewith examples described herein. The processing unit 58 may receive inputsignals x₁(n), x₂(n), x_(k)(n) (e.g. X(n)) 60 a-c for processing, e.g.,as a component of a MIMO wireless transceiver. The processing unit 58may include multiplication unit/accumulation units 62 a-c, 66 a-c andmemory lookup units 64 a-c, 68 a-c that, when mixed with input signals,may generate output signals z₁(n), z₂(n), z_(l)(n) (e.g. Z(n))) 70 a-c.In some examples, the output signals (e.g. Z(n)) 70 a-c may be utilizedas the output of a component of the MEMO wireless transceiver. Theprocessing unit 58, may be provided instructions to cause the processingunit 58 to configure the multiplication units 62 a-c to multiply inputsignals 60 a-c with ordered sets of respective ordered neurons andconnections weights to generate multiplication processing result to besummed. The accumulation units 66 a-c are configured to the productvalues to generate the output signals 70 a-c.

The multiplication unit/accumulation units 62 a-c, 66 a-c multiply twooperands from the input signals 60 a-c to generate a multiplicationprocessing result that is accumulated by the accumulation unit portionof the multiplication unit/accumulation units 62 a-c, 66 a-c. Themultiplication unit/accumulation units 62 a-c, 66 a-c adds themultiplication processing result to update the processing result storedin the accumulation unit portion, thereby accumulating themultiplication processing result. For example, the multiplicationunit/accumulation units 62 a-c, 66 a-c may perform a multiply-accumulateoperation such that two operands, M and N, are multiplied and then addedwith P to generate a new version of P that is stored in its respectivemultiplication unit/accumulation units.

The memory look-up units 64 a-c, 68 a-c retrieve ordered sets of orderedneurons and/or connections weights stored in memory 55. The output ofthe memory look-up units 64 a-c, 68 a-c is provided to themultiplication unit/accumulation units 62 a-c, 66 a c that may beutilized as a multiplication operand in the multiplication unit portionof the multiplication unit/accumulation units 62 a-c, 66 a-c. Forexample, the memory look-up unit can be a table look-up that retrieves aspecific plurality of connection weights associated with that respectiveordered neuron. As described herein, the neuron calculator 18 maycalculate, dynamically, the ordered sets of the ordered neurons based onthe input signals 60 a-c to be used as part of the multiply-accumulateoperation. In some examples, the calculated ordered sets may be storedin the memory 55 and retrieved by the memory look-up units 64 a-c, 68a-c. Or the calculated ordered sets may be utilized in themultiply-accumulate operation, once calculated, as part of generatingthe output signals 70 a-c. For example, the input signals 60 a-c may beused to calculate respective ordered sets, e.g., inputs signals for asecond-order neuron comprises second-order p_(ij) elements as describedabove with respect to FIG. 1A. Accordingly, in various examples ofcalculating ordered sets, the circuitry arrangement of FIG. 1B mayutilized to generate the output signals (e.g. Z(n)) 70 a-c from theinput signals (e.g. X(n)) 60 a-c.

Each of the multiplication unit/accumulation units 62 a-c, 66 a-c mayinclude multiple multipliers, multiple accumulation unit, or and/ormultiple adders. Any one of the multiplication unit/accumulation units62 a-c, 66 a-c may be implemented using an ALU. In some examples, anyone of the multiplication unit/accumulation units 62 a-c, 66 a-c caninclude one multiplier and one adder that each perform, respectively,multiple multiplications and multiple additions. The input-outputrelationship of a multiplication/accumulation unit 62 a-c, 66 a-c may berepresented as:

$\begin{matrix}{B_{out} = {\sum\limits_{i = 1}^{I}\;{C_{i}*{B_{in}(i)}}}} & (6)\end{matrix}$where “I” represents a number to perform the multiplications in thatunit, C_(i) the coefficients which may be accessed from a memory, suchas memory 55, and B_(in)(i) represents a factor from either the inputdata X(n) 60 a-c or an output from multiplication unit/accumulationunits 62 a-c, 66 a-c. In an example, the output of a set ofmultiplication unit/accumulation units, B_(out), equals the sum ofcoefficient data, C_(i) multiplied by the output of another set ofmultiplication unit/accumulation units, B_(in)(i). B_(in)(i) may also bethe input data such that the output of a set of multiplicationunit/accumulation units, B_(out), equals the sum of coefficient data,C_(i) multiplied by input data.

FIG. 2 is a schematic illustration of a system arranged in accordancewith examples described herein. System 100 includes electronic device102, electronic device 110, antenna 101, antenna 103, antenna 105,antenna 107, antenna 121, antenna 123, antenna 125, antenna 127,wireless transmitter 131, wireless transmitter 133, wireless receiver135 and, wireless receiver 137. Antennas 101, 103, 105, 107, 121, 123,125, and 127 may be dynamically tuned to different frequencies or bands,in some examples. The electronic device 102 may include antenna 121associated with a first frequency, antenna 123 associated with a secondfrequency, antenna 125 associated with the first frequency, antenna 127associated with the second frequency, wireless transmitter 131 for thefirst frequency, wireless transmitter 133 for the second frequency,wireless receiver 135 for the first frequency, and wireless receiver 137the second frequency. The electronic device 110 may include the antenna101 associated with the first frequency, antenna 103 associated with thesecond frequency, antenna 105 associated with the first frequency,antenna 107 associated with the second frequency, wireless transmitter111 for the first frequency, wireless transmitter 113 for the secondfrequency, wireless receiver 115 for the first frequency, and wirelessreceiver 117 for the second frequency.

Electronic devices 102, 110 may include a neural network 10. Forexample, wireless transmitter 131 and wireless receiver 135 may includein combination a neural network 10, each having a neuron calculator 18incorporated as part of at least on component of the respectivetransmitter 131 or receiver 135, In operation, the neuron calculators 18may calculate ordered sets and provide output signals for one or morecomponents of the transmitter 131 or the receiver 135. In an example,the wireless transmitter 133 may include a neural network 10 withseveral neuron calculators 18 or a single neuron calculator 18. Inoperation, the neuron calculator(s) 18 of the transmitter 133 maycalculate ordered sets and provide output signals for one or morecomponents of the transmitter 133. As can be appreciated, and asadditionally described with respect to FIG. 5 for a MIMO transceiverapplication, neuron calculators 18 may be implemented in variousportions of electronic devices 102, 110, as individual components ofcertain aspects of the electronic devices or working together in aneural network 10 including various neuron calculators 18.

Electronic devices described herein, such as electronic device 102 andelectronic device 110 shown in FIG. 2 may be implemented using generallyany electronic device for which communication capability is desired. Forexample, electronic device 102 and/or electronic device 110 may beimplemented using a mobile phone, smartwatch, computer (e.g. server,laptop, tablet, desktop), or radio. In some examples, the electronicdevice 102 and/or electronic device 110 may be incorporated into and/orin communication with other apparatuses for which communicationcapability is desired, such as but not limited to, a wearable device, amedical device, an automobile, airplane, helicopter, appliance, tag,camera, or other device.

While not explicitly shown in FIG. 2, electronic device 102 and/orelectronic device 110 may include any of a variety of components in someexamples, including, but not limited to, memory, input/output devices,circuitry, processing units (e.g. processing elements and/orprocessors), or combinations thereof.

The electronic device 102 and the electronic device 110 may each includemultiple antennas. For example, the electronic device 102 and electronicdevice 110 may each have more than two antennas. Three antennas each areshown in FIG. 2, but generally any number of antennas may be usedincluding 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 32, or 64antennas. Other numbers of antennas may be used in other examples. Insome examples, the electronic device 102 and electronic device 110 mayhave a same number of antennas, as shown in FIG. 2. In other examples,the electronic device 102 and electronic device 110 may have differentnumbers of antennas.

Generally, systems described herein may include multiple-input,multiple-output (“MIMO”) systems. MIMO systems generally refer tosystems including one or more electronic devices which transmittransmissions using multiple antennas and one or more electronic deviceswhich receive transmissions using multiple antennas. In some examples,electronic devices may both transmit and receive transmissions usingmultiple antennas. Some example systems described herein may be “massiveMIMO” systems. Generally, massive MIMO systems refer to systemsemploying greater than a certain number (e.g. 16) antennas to transmitand/or receive transmissions. As the number of antennas increase, sogenerally does the complexity involved in accurately transmitting and/orreceiving transmissions.

Although two electronic devices electronic device 102 and electronicdevice 110) are shown in FIG. 2, generally the system 100 may includeany number of electronic devices.

Electronic devices described herein may include receivers, transmitters,and/or transceivers. For example, the electronic device 102 of FIG. 2includes wireless transmitter 131 and wireless receiver 135, and theelectronic device 110 includes wireless transmitter 111 and wirelessreceiver 115. Generally, receivers may be provided for receivingtransmissions from one or more connected antennas, transmitters may beprovided for transmitting transmissions from one or more connectedantennas, and transceivers may be provided for receiving andtransmitting transmissions from one or more connected antennas. Whileboth electronic devices 102, 110 are depicted in FIG. 2 with individualwireless transmitter and individual wireless receivers, it can beappreciated that a wireless transceiver may be coupled to antennas ofthe electronic device and operate as either a wireless transmitter orwireless receiver, to receive and transmit transmissions. For example, atransceiver of electronic device 102 may be used to providetransmissions to and/or receive transmissions from antennas 121 and 123,while other transceivers of electronic device 110 may be used to providetransmissions to and/or receive transmissions from antenna 101 andantenna 103.

Generally, multiple receivers, transmitters, and/or transceivers may beprovided in an electronic device—one in communication with each of theantennas of the electronic device. The transmissions may be inaccordance with any of a variety of protocols, including, but notlimited to 5G signals, and/or a variety of modulation/demodulationschemes may be used, including, but not limited to: orthogonal frequencydivision multiplexing (OFDM), filter bank multi-carrier (FBMC), thegeneralized frequency division multiplexing (GFDM), universal filteredmulti-carrier (UFMC) transmission, bi orthogonal frequency divisionmultiplexing (BFDM), sparse code multiple access (SOMA), non-orthogonalmultiple access (NOMA), multi-user shared access (MUSA) andfaster-than-Nyquist (FTN) signaling with time-frequency packing. In someexamples, the transmissions may be sent, received, or both, inaccordance with various protocols and/or standards (e.g., NR, LTE, WiFi,etc.).

Examples of transmitters, receivers, and/or transceivers describedherein, such as the wireless transmitter 131, wireless transmitter 133,wireless receiver 115, or wireless receiver 117, may be implementedusing a variety of components, including, hardware, software, firmware,or combinations thereof. For example, transceivers, transmitters, orreceivers may include circuitry and/or one or more processing units(e.g. processors) and memory encoded with executable instructions forcausing the transceiver to perform one or more functions describedherein (e.g. software).

FIG. 3 is a schematic illustration of a wireless transmitter 300. Thewireless transmitter 300 receives a data signal 311 and performsoperations to generate wireless communication signals for transmissionvia the antenna 303. The wireless transmitter 300 may be utilized toimplement the wireless transmitters 111, 113, 131, 133 of FIG. 2, forexample. The transmitter output signal x_(N)(n) 310 is amplified by apower amplifier 332 before the output data are transmitted on an RFantenna 303. The operations to the RF-front end may generally beperformed with analog circuitry or processed as a digital basebandoperation for implementation of a digital front-end. The operations ofthe baseband and RF-front end include a scrambler 304, a coder 308, aninterleaver 312, a modulation mapping 316, a frame adaptation 320, aninverse fast Fourier transform (IFFT) logic 324, a guard interval 328,and frequency up-conversion 330.

The scrambler 304 may convert the input data to a pseudo-random orrandom binary sequence. For example, the input data may be a transportlayer source (such as MPEG-2 Transport stream and other data) that isconverted to a Pseudo Random Binary Sequence (PRBS) with a generatorpolynomial. While described in the example of a generator polynomial,various scramblers 304 are possible.

The coder 308 may encode the data outputted from the scrambler to codethe data. For example, a Reed-Solomon (RS) encoder, turbo encoder may beused as a first coder to generate a parity block for each randomizedtransport packet fed by the scrambler 304. In some examples, the lengthof parity block and the transport packet can vary according to variouswireless protocols. The interleaver 312 may interleave the parity blocksoutput by the coder 308, for example, the interleaver 312 may utilizeconvolutional byte interleaving. In some examples, additional coding andinterleaving can be performed after the coder 308 and interleaver 312.For example, additional coding may include a second coder that mayfurther code data output from the interleaver, for example, with apunctured convolutional coding having a certain constraint length.Additional interleaving may include an inner interleaver that formsgroups of joined blocks. While described in the context of a RS coding,turbo coding, and punctured convolution coding, various coders 308 arepossible, such as a low-density parity-check (LDPC) coder or a polarcoder. While described in the context of convolutional byteinterleaving, various interleavers 312 are possible.

The modulation mapping 316 may modulate the data output from theinterleaver 312. For example, quadrature amplitude modulation (QAM) maybe used to map the data by changing (e.g., modulating) the amplitude ofthe related carriers. Various modulation mappings may be used,including, but not limited to: Quadrature Phase Shift Keying(QPSK),SCMA, NOMA, and MUSA (Multi-user Shared Access). Output from themodulation mapping 316 may be referred to as data symbols. Whiledescribed in the context of QAM modulation, various modulation mappings316 are possible. The frame adaptation 320 may arrange the output fromthe modulation mapping according to bit sequences that representcorresponding modulation symbols, carriers, and frames.

The IFFT logic 324 may be a processor and/or a computer-readable mediaimplementing instructions to execute an inverse fast Fourier transform.For example, the IFFT logic 324 may transform symbols that have beenframed into sub-carriers (e.g., by frame adaptation 320) intotime-domain symbols. Taking an example of a 5G wireless protocol scheme,the IFFT can be applied as N-point IFFT:

$\begin{matrix}{x_{k} = {\sum\limits_{n = 1}^{N}\;{X_{n}e^{i\; 2\pi\;{{kn}/N}}}}} & (7)\end{matrix}$where X_(n) is the modulated symbol sent in the nth 5G sub-carrier.Accordingly, the output of the IFFT logic 324 may form time-domain 5Gsymbols. In some examples, the IFFT of the logic 324 may be replaced bya pulse shaping filter or poly-phase filtering banks to output symbolsfor frequency up-conversion 330. For example, the processor and/or thecomputer-readable media implementing instructions to execute an inversefast Fourier transform may be changed or updated to implement a pulseshaping filter or poly-phase filtering banks.

In the example of FIG. 3, the guard interval 328 adds a guard intervalto the time-domain 5G symbols. For example, the guard interval may be afractional length of a symbol duration that is added, to reduceinter-symbol interference, by repeating a portion of the end of atime-domain 5G symbol at the beginning of the frame. For example, theguard interval can be a time period corresponding to the cyclic prefixportion of the 5G wireless protocol scheme.

The frequency up-conversion 330 may up-convert the time-domain 5Gsymbols to a specific radio frequency. For example, the time-domain 5Gsymbols can be viewed as a baseband frequency range and a localoscillator can mix the frequency at which it oscillates with the 5Gsymbols to generate 5G symbols at the oscillation frequency. A digitalup-converter (DUC) may also be utilized to convert the time-domain 5Gsymbols. Accordingly, the 5G symbols can be up-converted to a specificradio frequency for an RF transmission.

Before transmission, at the antenna 303, a power amplifier 332 mayamplify the transmitter output signal X_(N)(n) 310 to output data for anRF transmission in an RF domain at the antenna 303. The antenna 303 maybe an antenna designed to radiate at a specific radio frequency. Forexample, the antenna 303 may radiate at the frequency at which the 5Gsymbols were up-converted. Accordingly, the wireless transmitter 300 maytransmit an RF transmission via the antenna 303 based on the data signal311 received at the scrambler 304.

As described above with respect to FIG. 3, the operations of thewireless transmitter 300 can include a variety of processing operations.Such operations can be implemented in a conventional wirelesstransmitter, with each operation implemented by specifically-designedhardware for that respective operation. For example, a DSP processingunit may be specifically-designed to implement the guard interval 328.As described in examples herein, a neural calculator 18 may be includedin a wireless transmitter 300 to perform one or more of the processingoperations/components. Accordingly, a neural calculator 18 may implementthe guard interval 328. As can be appreciated, additional operations ofwireless transmitter 300 may be included in a conventional wirelesstransmitter, which are not depicted in FIG. 3 (e.g., andigital-to-analog converter (DAC)), but are also operations that aneural calculator 18 may implement.

FIG. 4 is a schematic illustration of wireless receiver 400. Thewireless receiver 400 receives input data X (i,j) 410 from an antenna405 and performs operations of a wireless receiver to generate receiveroutput data at the descrambler 444. The wireless receiver 400 may beutilized to implement the wireless receivers 115, 117, 135, 137 of FIG.2, for example. The antenna 405 may be an antenna designed to receive ata specific radio frequency. The operations of the wireless receiver maybe performed with analog circuitry or processed as a digital basebandoperation for implementation of a digital front-end. The operations ofthe wireless receiver include a frequency down-conversion 412, guardinterval removal 416, a fast Fourier transform (FFT) logic 420,synchronization 424, channel estimation 428, a demodulation mapping 432,a deinterleaver 436, a decoder 440, and a descrambler 444.

The frequency down-conversion 412 may down-convert the frequency domainsymbols to a baseband processing range. For example, continuing in theexample of a 5G implementation, the frequency-domain 5G symbols may bemixed with a local oscillator frequency to generate 5G symbols at abaseband frequency range. A digital down-converter (DDC) may also beutilized to convert the frequency domain symbols. Accordingly, the RFtransmission including time-domain 5G symbols may be down-converted tobaseband. The guard interval removal 416 may remove a guard intervalfrom the frequency-domain 5G symbols.

The FFT logic 420 may be a processor and/or a computer-readable mediaimplementing instructions to execute a fast Fourier transform. Forexample, the FFT logic 420 may transform the time-domain 5G symbols intofrequency-domain 5G symbols. Taking an example of a 5G wireless protocolscheme, the FFT can be applied as N-point FF:

$\begin{matrix}{X_{n} = {\sum\limits_{k = 1}^{N}{x_{k}e^{{- i}\; 2\pi\;{{kn}/N}}}}} & (8)\end{matrix}$where X_(n) is the modulated symbol sent in the nth 5G sub-carrier.Accordingly, the output of the FFT logic 420 may form frequency-domain5G symbols. In some examples, the FFT of the logic 420 may be replacedby poly-phase filtering banks to output symbols for synchronization 424.For example, the processor and/or the computer-readable mediaimplementing instructions to execute a fast Fourier transform may bechanged or updated to implement poly-phase filtering banks.

The synchronization 424 may detect pilot symbols in the 5G symbols tosynchronize the transmitted data. In some examples of a 5Gimplementation, pilot symbols may be detected at the beginning of aframe (e.g., in a header) in the time-domain. Such symbols can be usedby the wireless receiver 400 for frame synchronization. With the framessynchronized, the 5G symbols proceed to channel estimation 428. Thechannel estimation 428 may also use the time-domain pilot symbols andadditional frequency-domain pilot symbols to estimate the time orfrequency effects (e.g., path loss) to the received signal.

For example, a channel may be estimated according to N signals receivedthrough M antennas (in addition to the antenna 405) in a preamble periodof each signal. In some examples, the channel estimation 428 may alsouse the guard interval that was removed at the guard interval removal416. With the channel estimate processing, the channel estimation 428may compensate for the frequency-domain 5G symbols by some factor tominimize the effects of the estimated channel. While channel estimationhas been described in terms of time-domain pilot symbols andfrequency-domain pilot symbols, other channel estimation techniques orsystems are possible, such as a MIMO-based channel estimation system ora frequency-domain equalization system.

The demodulation mapping 432 may demodulate the data outputted from thechannel estimation 428. For example, a quadrature amplitude modulation(QAM) demodulator can map the data by changing (e.g., modulating) theamplitude of the related carriers. Any modulation mapping describedherein can have a corresponding demodulation mapping as performed bydemodulation mapping 432. In some examples, the demodulation mapping 432may detect the phase of the carrier signal to facilitate thedemodulation of the 5G symbols. The demodulation mapping 432 maygenerate bit data from the 5G symbols to be further processed by thedeinterleaver 436.

The deinterleaver 436 may deinterleave the data bits, arranged as parityblock from demodulation mapping into a bit stream for the decoder 440,for example, the deinterleaver 436 may perform an inverse operation toconvolutional byte interleaving. The deinterleaver 436 may also use thechannel estimation to compensate for channel effects to the parityblocks.

The decoder 440 may decode the data outputted from the scrambler to codethe data. For example, a Reed-Solomon (RS) decoder or turbo decoder maybe used as a decoder to generate a decoded bit stream for thedescrambler 444. For example, a turbo decoder may implement a parallelconcatenated decoding scheme. In some examples, additional decodingand/or deinterleaving may be performed after the decoder 440 anddeinterleaver 436. For example, additional decoding may include anotherdecoder that may further decode data output from the decoder 440. Whiledescribed in the context of a RS decoding and turbo decoding, variousdecoders 440 are possible, such as low-density parity-check (LDPC)decoder or a polar decoder.

The descrambler 444 may convert the output data from decoder 440 from apseudo-random or random binary sequence to original source data. Forexample, the descrambler 44 may convert decoded data to a transportlayer destination (e.g., MPEG-2 transport stream) that is descrambledwith an inverse to the generator polynomial of the scrambler 304. Thedescrambler thus outputs receiver output data. Accordingly, the wirelessreceiver 400 receives an RF transmission including input data X (i,j)410 via to generate the receiver output data.

As described herein, for example with respect to FIG. 4, the operationsof the wireless receiver 400 can include a variety of processingoperations. Such operations can be implemented in a conventionalwireless receiver, with each operation implemented byspecifically-designed hardware for that respective operation. Forexample, a DSP processing unit may be specifically-designed to implementthe FFT 420. As described in examples herein, a neural calculator 18 maybe included in a wireless receiver 400 to perform one or more of theprocessing operations/components. Accordingly, a neural calculator 18may implement the FFT 420. As can be appreciated, additional operationsof wireless receiver 400 may be included in a conventional wirelessreceiver, which are not depicted in FIG. 4 (e.g., an analog-to-digitalconverter (ADC)), but are also operations that a neural calculator 18may implement.

FIG. 5 is a schematic illustration 200 of an electronic device 110arranged in accordance with examples described herein. Similarly,numbered elements of FIG. 5 include analogous functionality to thosenumbered elements of FIG. 2. The electronic device 110 may also includea neuron calculator 240, which may be the neuron calculator 18. Eachwireless transmitter 111, 113 may be in communication with a respectiveantenna, such as antenna 101, antenna 103. Each wireless transmitter111, 113 receives a respective data signal, such as data signals 211,213. The wireless transmitter 113 may process the data signal 213 withthe operations of a wireless transmitter e.g., transmitter 300) togenerate a transmission signal (e.g., output signal x_(N)(n) 310). Eachwireless receiver 115, 117 may be in communication with a respectiveantenna, such as antenna 105, antenna 107. Each wireless receiver 115,117 receives respective signals from the antennas 105, 107; and mayprocess signals with the operations of a wireless receiver (e.g.,wireless receiver 400) to generate received output signals 255, 257.

During processing of the signals received from the antennas 105, 107,the wireless receivers 115, 117 may provide input signals x₁(n), x₂(n)221, 223 to the neuron calculator 240. For example, the input signalsx₁(n), x₂(n) 221, 223 may be provided to the neuron calculator 240 viainternal paths from an output of the wireless receiver 115 and an outputof the wireless receiver 117. Accordingly, paths stemming from thewireless receivers 115, 117 and the neuron calculator 240 may be incommunication with one another. The neuron calculator 240, therefore,receives a first signal x₁(n) 221 associated with the wireless receiver115 and a second signal x₂(n) 223 associated with the wireless receiver117.

Examples of neuron calculators described herein may generate and provideoutput signals z₁(n), z₂(n) 245, 247 to wireless receivers 245, 247. Ingenerating such output signals, the neuron calculator may calculateelements of ordered sets p_(ij) ^((k)) 241. For example, as describedwith reference to FIG. 1A, various ordered sets may be calculated basedon the input signals x₁(n), x₂(n) 221, 223. In some examples where theinputs signals are calibration signals, the neuron calculator 240 mayalso determine connection weights in accordance with Equation 1-5. So,for example, the neuron calculator 240 may generate and store connectionweights in a local memory of the electronic device 110 and using suchweights may provide output signals z₁(n), z₂(n) 245, 247 to wirelessreceivers 115, 117. Continuing in an example of the neuron calculator 18having been provided the input signals x₁(n), x₂(n) 221, 223, the neuroncalculator 18 may be configured to perform a functionality of thewireless receivers 115, 117. For example, the neuron calculator 240 mayperform a channel estimation (e.g., channel estimation 428) for thewireless receivers 115, 117 on the input signals x₁(n), x₂(n) 221, 223to provide output signals z₁(n), z₂(n) 245, 247 with a removed orreduced error introduced by a wireless channel(s) (e.g., wirelesschannels associated with the first and second frequencies). The neuroncalculator 240 may mix the input signals x₁(n), x₂(n) 221, 223 with theordered sets of ordered neurons and connection weights to calculate theoutput signals z₁(n), z₂(n) 245, 247. In the example, the neuroncalculator 240 may receive the input signals x₁(n), x₂(n) 221, 223 assymbols from the wireless receivers 115, 117; and, thus, provide outputsignals z₁(n), z₂(n) 245, 247 that may be referred to as compensatedsymbols. For example, the output signals may be compensated because achannel error present in the signals x₁(n), x₂(n) 221, 223 has beenremoved or reduced.

While FIG. 5 depicts neuron calculator 240 operating on signals from thewireless receivers 115, 117 at a channel estimation stage/component ofthe wireless receiver stage, it can be appreciated that various signals,whether amplified, modulated, or initial, may be provided to a neuroncalculator 18, such as neuron calculator 240, to perform a functionalityof one or more processing stages of the wireless receivers 115, 117. Forexample, in an embodiment, a neuron calculator may receive each of theinput signals x₁(n), x₂(n) 221, 223 at a decoder stage of the wirelessreceiver (e.g., decoder 440). In various examples, input signals may beprovided at varying points in a receiver path. Additionally oralternatively, neuron calculator 240 may communicate with wirelesstransmitters 111, 113 to perform a functionality of one or moreprocessing stages of the wireless transmitters 111, 113,

FIG. 6 is a flowchart of a method 600 in accordance with examplesdescribed herein. Example method 600 may be implemented using, forexample, in electronic device 102, 110 of FIG. 2, electronic device 110of FIG. 5, or any system or combination of the systems depicted in FIG.2, FIG. 5, and FIGS. 7-9 described herein. In some examples, the blocksin example method 600 may be performed by a neuron calculator 18implemented as processing unit 58. The operations described in blocks608-628 may also be stored as control instructions in acomputer-readable medium such as memory 55 or in an electronic device110 including a memory.

Example method 600 may begin a neuron calculation method. At block 608,the method 600 includes receiving calibration signals at a neuroncalculator. A neuron calculator 18 having inputs 20, 22, and 28 mayreceive at least respective calibration signals at each input, e.g., afirst calibration signal, a second calibration signal, and a thirdcalibration signal. Such calibration signals may be utilized todetermine connection weights for the neuron calculator, as furtherdescribed with respect to block 620. For example, a set of calibrationsignals may include a signal utilized for a wireless transmitter orwireless receiver to determine a channel estimation, e.g., a pilotsignal.

At block 612, the method 600 includes calculating a plurality of orderedsets based on the calibration signals. For example, as described withrespect to Table 1, calculating the plurality of ordered sets includes,multiplying each of first calibration signal, second calibration signal,and third calibration signal with one of the first calibration signal,second calibration signal, or third calibration signal to generate asecond-order set of the plurality of ordered sets. Similarly, for athird-order set calculation, as described with respect to Table 2,calculating the plurality of ordered sets includes, multiplying each ofthe first calibration signal, second calibration signal, and thirdcalibration signal with two signals of a set including the firstcalibration signal, second calibration signal, or third calibrationsignal to generate the third-order set. For example, with respect to thesecond-order set, multiplying each of first calibration signal, secondcalibration signal, and third calibration signal with one of the firstcalibration signal, second calibration signal, or third calibrationsignal includes multiplying the first calibration signal with the firstcalibration signal to generate a first multiplicative processing resultof the second order set; multiplying the first calibration signal withthe second calibration signal to generate a second multiplicativeprocessing result of the second order set; multiplying the firstcalibration signal with the third calibration signal to generate a thirdmultiplicative processing result of the second order set; multiplyingthe second calibration signal with the first calibration signal togenerate a fourth multiplicative processing result of the second orderset; multiplying the second calibration signal with the secondcalibration signal to generate a fifth multiplicative processing resultof the second order set; multiplying the second calibration signal withthe third calibration signal to generate a sixth multiplicativeprocessing result of the second order set; multiplying the thirdcalibration signal with the first calibration signal to generate aseventh multiplicative processing result of the second order set;multiplying the third calibration signal with the second calibrationsignal to generate an eighth multiplicative processing result of thesecond order set; and multiplying the third calibration signal with thethird calibration signal to generate a ninth multiplicative processingresult of the second order set.

At block 616, the method 600 includes allocating each ordered set of theplurality of ordered sets to a respective ordered neuron of the neuroncalculator. For example, as described with respect to FIGS. 1A and 1B,the neuron calculator 18 comprises a plurality of processing unitsconfigured to process signals in accordance with respective orderedneurons. Each ordered neuron 30, 32, and 38 may be implemented at arespective processing unit 58. Or, in some examples, all ordered neurons30, 32, and 38 may be implemented at a single processing unit 58. Inallocating the ordered sets to the ordered neurons, the neuroncalculator, or multiple neuron calculators 18 in a neural network 10,determine that calculated ordered sets are allocated to one or moreprocessing units, to respective ordered neurons, for further calculationof the input signals with connection weights to generate output signals.

At block 620, the method 600 includes generating connection weights forthe neuron calculator. The neuron calculator may utilize an algorithm toimplement Equations 1-5 to generate the connection weights. For example,using a gradient descent method, connection weights may be randomlyselected and iterated at a learning rate factor until a convergencepoint is reached. A connection weight may be determined for acorresponding connection between each respective ordered neuron of theneuron calculator and a respective output of a plurality of outputs ofthe neuron calculator. At the outputs, at least a portion of theplurality of ordered sets may be combined/mixed with at least a portionof the connection weights to generate compensated calibration signals.In iterating, an error of compensated calibrations signals based on asummation of the plurality of connection weights and at least a portionof the plurality of ordered sets may be reduced. At block 628, themethod 600 ends.

The blocks included in the described example methods 600 are forillustration purposes. In some examples, the blocks may be performed ina different order. In some other examples, various blocks may beeliminated. In still other examples, various blocks may be divided intoadditional blocks, supplemented with other blocks, or combined togetherinto fewer blocks. Other variations of these specific blocks arecontemplated, including changes in the order of the blocks, changes inthe content of the blocks being split or combined into other blocks,etc.

FIG. 7 illustrates an example of a wireless communications system 700 inaccordance with aspects of the present disclosure. The wirelesscommunications system 700 includes a base station 710, a mobile device715, a drone 717, a small cell 730, and vehicles 740, 745. The basestation 710 and small cell 730 may be connected to a network thatprovides access to the Internet and traditional communication links. Thesystem 700 may facilitate a wide-range of wireless communicationsconnections in a 5G wireless system that may include various frequencybands, including but not limited to: a sub-6 GHz band (e.g., 700 MHzcommunication frequency), mid-range communication bands (e.g., 2.4 GHz),and mmWave bands (e.g., 24 GHz).

Additionally or alternatively, the wireless communications connectionsmay support various modulation schemes, including hut not limited to:filter bank multi-carrier (FBMC), the generalized frequency divisionmultiplexing (GFDM), universal filtered multi-carrier (UFMC)transmission, bi-orthogonal frequency division multiplexing (BFDM),sparse code multiple access (SCMA), non-orthogonal multiple access(NOMA), multi-user shared access (MUSA), and faster-than-Nyquist (FTN)signaling with time-frequency packing. Such frequency bands andmodulation techniques may be a part of a standards framework, such asLong Term Evolution (LTE) or other technical specification published byan organization like 3GPP or IEEE, which may include variousspecifications for subcarrier frequency ranges, a number of subcarriers,uplink/downlink transmission speeds, TDD/FDD, and/or other aspects ofwireless communication protocols.

The system 700 may depict aspects of a radio access network (RAN), andsystem 700 may be in communication with or include a core network (notshown). The core network may include one or more serving gateways,mobility management entities, home subscriber servers, and packet datagateways. The core network may facilitate user and control plane linksto mobile devices via the RAN, and it may be an interface to an externalnetwork (e.g., the Internet). Base stations 710, communication devices720, and small cells 730 may be coupled with the core network or withone another, or both, via wired or wireless backhaul links (e.g., S1interface, X2 interface, etc.).

The system 700 may provide communication links connected to devices or“things,” such as sensor devices, e.g., solar cells 737, to provide anInternet of Things (“IoT”) framework. Connected things within the IoTmay operate within frequency bands licensed to and controlled bycellular network service providers, or such devices or things may. Suchfrequency bands and operation may be referred to as narrowband IoT(NB-IoT) because the frequency bands allocated for IoT operation may besmall or narrow relative to the overall system bandwidth. Frequencybands allocated for NB-IoT may have bandwidths of 50, 100, or 200 KHz,for example.

Additionally or alternatively, the IoT may include devices or thingsoperating at different frequencies than traditional cellular technologyto facilitate use of the wireless spectrum. For example, an IoTframework may allow multiple devices in system 700 to operate at a sub-6GHz band or other industrial, scientific, and medical (ISM) radio bandswhere devices may operate on a shared spectrum for unlicensed uses. Thesub-6 GHz band may also be characterized as and may also becharacterized as an NB-IoT band. For example, in operating at lowfrequency ranges, devices providing sensor data for “things,” such assolar cells 737, may utilize less energy, resulting in power-efficiencyand may utilize less complex signaling frameworks, such that devices maytransmit asynchronously on that sub-6 GHz band. The sub-6 GHz band maysupport a wide variety of uses case, including the communication ofsensor data from various sensors devices. Examples of sensor devicesinclude sensors for detecting energy, heat, light, vibration, biologicalsignals (e.g., pulse, EEG, EKG, heart rate, respiratory rate, bloodpressure), distance, speed, acceleration, or combinations thereof.Sensor devices may be deployed on buildings, individuals, and/or inother locations in the environment. The sensor devices may communicatewith one another and with computing systems which may aggregate and/oranalyze the data provided from one or multiple sensor devices in theenvironment. Such data may be used to indicate an environmentalcharacteristic of the sensor.

In such a 5G framework, devices may perform functionalities performed bybase stations in other mobile networks (e.g., UMTS or LTE), such asforming a connection or managing mobility operations between nodes(e.g., handoff or reselection). For example, mobile device 715 mayreceive sensor data from the user utilizing the mobile device 715, suchas blood pressure data, and may transmit that sensor data on anarrowband IoT frequency band to base station 710. In such an example,some parameters for the determination by the mobile device 715 mayinclude availability of licensed spectrum, availability of unlicensedspectrum, and/or time-sensitive nature of sensor data. Continuing in theexample, mobile device 715 may transmit the blood pressure data becausea narrowband IoT band is available and can transmit the sensor dataquickly, identifying a time-sensitive component to the blood pressure(e.g., if the blood pressure measurement is dangerously high or low,such as systolic blood pressure is three standard deviations from norm).

Additionally or alternatively, mobile device 715 may formdevice-to-device (D2D) connections with other mobile devices or otherelements of the system 700. For example, the mobile device 715 may formRFID, WiFi, MultiFire, Bluetooth, or Zigbee connections with otherdevices, including communication device 720 or vehicle 745. In someexamples, D2D connections may be made using licensed spectrum bands, andsuch connections may be managed by a cellular network or serviceprovider. Accordingly, while the above example was described in thecontext of narrowband IoT, it can be appreciated that otherdevice-to-device connections may be utilized by mobile device 715 toprovide information (e.g., sensor data) collected on different frequencybands than a frequency band determined by mobile device 715 fortransmission of that information.

Moreover, some communication devices may facilitate ad-hoc networks, forexample, a network being formed with communication devices 720 attachedto stationary objects) and the vehicles 740, 745, without a traditionalconnection to a base station 710 and/or a core network necessarily beingformed. Other stationary objects may be used to support communicationdevices 720, such as, but not limited to, trees, plants, posts,buildings, blimps, dirigibles, balloons, street signs, mailboxes, orcombinations thereof. In such a system 700, communication devices 720and small cell 730 (e.g., a small cell, femtocell, WLAN access point,cellular hotspot, etc.) may be mounted upon or adhered to anotherstructure, such as lampposts and buildings to facilitate the formationof ad-hoc networks and other IoT-based networks. Such networks mayoperate at different frequency bands than existing technologies, such asmobile device 715 communicating with base station 710 on a cellularcommunication band.

The communication devices 720 may form wireless networks, operating ineither a hierarchal or ad-hoc network fashion, depending, in part, onthe connection to another element of the system 700. For example, thecommunication devices 720 may utilize a 700 MHz communication frequencyto form a connection with the mobile device 715 in an unlicensedspectrum, while utilizing a licensed spectrum communication frequency toform another connection with the vehicle 745. Communication devices 720may communicate with vehicle 745 on a licensed spectrum to providedirect access for time-sensitive data, for example, data for anautonomous driving capability of the vehicle 745 on a 5.9 GHz band ofDedicated Short Range Communications (DSRC).

Vehicles 740 and 745 may form an ad-hoc network at a different frequencyband than the connection between the communication device 720 and thevehicle 745. For example, for a high bandwidth connection to providetime-sensitive data between vehicles 740, 745, a 24 GHz mmWave band maybe utilized for transmissions of data between vehicles 740, 745. Forexample, vehicles 740, 745 may share real-time directional andnavigation data with each other over the connection while the vehicles740, 745 pass each other across a narrow intersection line. Each vehicle740, 745 may be tracking the intersection line and providing image datato an image processing algorithm to facilitate autonomous navigation ofeach vehicle while each travels along the intersection line. In someexamples, this real-time data may also be substantially simultaneouslyshared over an exclusive, licensed spectrum connection between thecommunication device 720 and the vehicle 745, for example, forprocessing of image data received at both vehicle 745 and vehicle 740,as transmitted by the vehicle 740 to vehicle 745 over the 24 GHz mmWaveband. While shown as automobiles in FIG. 7, other vehicles may be usedincluding, but not limited to, aircraft, spacecraft, balloons, blimps,dirigibles, trains, submarines, boats, ferries, cruise ships,helicopters, motorcycles, bicycles, drones, or combinations thereof.

While described in the context of a 24 GHz mmWave band, it can beappreciated that connections may be formed in the system 700 in othermmWave bands or other frequency bands, such as 28 GHz, 37 GHz, 38 GHz,39 GHz, which may be licensed or unlicensed bands. In some cases,vehicles 740, 745 may share the frequency band that they arecommunicating on with other vehicles in a different network. Forexample, a fleet of vehicles may pass vehicle 740 and, temporarily,share the 24 GHz mmWave band to form connections among that fleet, inaddition to the 24 GHz mmWave connection between vehicles 740, 745. Asanother example, communication device 720 may substantiallysimultaneously maintain a 700 MHz connection with the mobile device 715operated by a user (e.g., a pedestrian walking along the street) toprovide information regarding a location of the user to the vehicle 745over the 5.9 GHz band. In providing such information, communicationdevice 720 may leverage antenna diversity schemes as part of a massiveMIMO framework to facilitate time-sensitive, separate connections withboth the mobile device 715 and the vehicle 745. A massive MIMO frameworkmay involve a transmitting and/or receiving devices with a large numberof antennas (e.g., 12, 20, 64, 128, etc.), which may facilitate precisebeamforming or spatial diversity unattainable with devices operatingwith fewer antennas according to legacy protocols (e.g., WiFi or LTE).

The base station 710 and small cell 730 may wirelessly communicate withdevices in the system 700 or other communication-capable devices in thesystem 700 having at the least a sensor wireless network, such as solarcells 737 that may operate on an active/sleep cycle, and/or one or moreother sensor devices. The base station 710 may provide wirelesscommunications coverage for devices that enter its coverages area, suchas the mobile device 715 and the drone 717. The small cell 730 mayprovide wireless communications coverage for devices that enter itscoverage area, such as near the building that the small cell 730 ismounted upon, such as vehicle 745 and drone 717.

Generally, the small cell 730 may be referred to as a small cell andprovide coverage for a local geographic region, for example, coverage of200 meters or less in some examples. This may be contrasted with amacrocell, which may provide coverage over a wide or large area on theorder of several square miles or kilometers. In some examples, a smallcell 730 may be deployed (e.g., mounted on a building) within somecoverage areas of a base station 710 (e.g., a macrocell) where wirelesscommunications traffic may be dense according to a traffic analysis ofthat coverage area. For example, a small cell 730 may be deployed on thebuilding in FIG. 7 in the coverage area of the base station 710 if thebase station 710 generally receives and/or transmits a higher amount ofwireless communication transmissions than other coverage areas of thatbase station 710. A base station 710 may be deployed in a geographicarea to provide wireless coverage for portions of that geographic area.As wireless communications traffic becomes denser, additional basestations 710 may be deployed in certain areas, which may alter thecoverage area of an existing base station 710, or other support stationsmay be deployed, such as a small cell 730. Small cell 730 may be afemtocell, which may provide coverage for an area smaller than a smallcell (e.g., 100 meters or less in some examples (e.g., one story of abuilding)).

While base station 710 and small cell 730 may provide communicationcoverage for a portion of the geographical area surrounding theirrespective areas, both may change aspects of their coverage tofacilitate faster wireless connections for certain devices. For example,the small cell 730 may primarily provide coverage for devicessurrounding or in the building upon which the small cell 730 is mounted.However, the small cell 730 may also detect that a device has entered iscoverage area and adjust its coverage area to facilitate a fasterconnection to that device.

For example, a small cell 730 may support a massive MIMO connection withthe drone 717, which may also be referred to as an unmanned aerialvehicle (UAV), and, when the mobile device 715 enters it coverage area,the small cell 730 adjusts some antennas to point directionally in adirection of the device 715, rather than the drone 717, to facilitate amassive MIMO connection with the vehicle, in addition to the drone 717.In adjusting some of the antennas, the small cell 730 may not support asfast as a connection to the drone 717, as it had before the adjustment.However, the drone 717 may also request a connection with another device(e.g., base station 710) in its coverage area that may facilitate asimilar connection as described with reference to the small cell 730, ora different (e.g., faster, more reliable) connection with the basestation 710. Accordingly, the small cell 730 may enhance existingcommunication links in providing additional connections to devices thatmay utilize or demand such links. For example, the small cell 730 mayinclude a massive MIMO system that directionally augments a link tovehicle 745, with antennas of the small cell directed to the vehicle 745for a specific time period, rather than facilitating other connections(e.g., the small cell 730 connections to the base station 710, drone717, or solar cells 737). In some examples, drone 717 may serve as amovable or aerial base station.

The wireless communications system 700 may include devices such as basestation 710, communication device 720, and small cell 730 that maysupport several connections to devices in the system 700. Such devicesmay operate in a hierarchal mode or an ad-hoc mode with other devices inthe network of system 700. While described in the context of a basestation 710, communication device 720, and small cell 730, it can beappreciated that other devices that can support several connections withdevices in the network may be included in system 700, including but notlimited to: macrocells, femtocells, routers, satellites, and MDdetectors.

In various examples, the elements of wireless communication system 700,such as the drone 717, may be implemented utilizing the systems,apparatuses, and methods described herein. For example, the drone 717,being implemented as the electronic device 110, may receive a wirelesscommunication signal from base station 710. In demodulating and decodingthe received wireless communications signal, the drone 717 may alsoimplement a neuron calculator 18 to calculate output signals for one ormore processing stages of a wireless receiver path. For example, thedrone 717 may implement the neuron calculator 18 for channel estimationto determine an error introduced by the wireless channel between thebase station 710 and the drone 717. In calculating the output signalsfor channel estimation as part of a neuron calculator 18, the drone 717may utilize less-power and less-memory, as the ordered sets of theneuron calculator 18 are calculated based on the received wirelesscommunications signal from the base station 710. Accordingly, the drone717 may utilize less die space on a silicon chip than conventionalsignal processing systems and techniques that can include additionalhardware or specially-designed hardware, thereby allowing the drone 717to be of smaller size compared to drones having such conventional signalprocessing systems and techniques.

Additionally or alternatively, while described in the examples above inthe context of the drone 717, the elements of communication system 700may be implemented as part of any example described herein, such aselectronic device 102, 110 of FIG. 2, electronic device 110 of FIG. 5,or any system or combination of the systems depicted in the Figuresdescribed herein.

FIG. 8 illustrates an example of a wireless communications system 800 inaccordance with aspects of the present disclosure. The wirelesscommunications system 800 includes a mobile device 815, a drone 817, acommunication device 820, and a small cell 830. A building 810 alsoincludes devices of the wireless communications system 800 that may beconfigured to communicate with other elements in the building 810 or thesmall cell 830. The building 810 includes networked workstations 840,845, virtual reality device 850, IoT devices 855, 860, and networkedentertainment device 865. In the depicted wireless communications system800, IoT devices 855, 860 may be a washer and dryer, respectively, forresidential use, being controlled by the virtual reality device 850.Accordingly, while the user of the virtual reality device 850 may be indifferent room of the building 810, the user may control an operation ofthe IoT device 855, such as configuring a washing machine setting.Virtual reality device 850 may also control the networked entertainmentdevice 865. For example, virtual reality device 850 may broadcast avirtual game being played by a user of the virtual reality device 850onto a display of the networked entertainment device 865.

The small cell 830 or any of the devices of building 810 may beconnected to a network that provides access to the Internet andtraditional communication links. Like the system 700, the wirelesscommunications system 800 may facilitate a wide-range of wirelesscommunications connections in a 5G system that may include variousfrequency bands, including but not limited to: a sub-6 GHz band (e.g.,700 MHz communication frequency), mid-range communication bands (e.g.,2.4 GHz), and mmWave bands (e.g., 24 GHz). Additionally oralternatively, the wireless communications connections may supportvarious modulation schemes as described above with reference to system700. Wireless communications system 800 may operate and be configured tocommunicate analogously to system 700. Accordingly, similarly numberedelements of wireless communications system 800 and system 700 may beconfigured in an analogous way, such as communication device 720 tocommunication device 820, small cell 730 to small cell 830, etc.

Like the system 700, where elements of system 700 are configured to formindependent hierarchal or ad-hoc networks, communication device 820 mayform a hierarchal network with small cell 830 and mobile device 815,while an additional ad-hoc network may be formed among the small cell830 network that includes drone 817 and some of the devices of thebuilding 810, such as networked workstations 840, 845 and IoT devices855, 860.

Devices in wireless communications system 800 may also form (D2D)connections with other mobile devices or other elements of the wirelesscommunications system 800. For example, the virtual reality device 850may form a narrowband IoT connections with other devices, including IoTdevice 855 and networked entertainment device 865. As described above,in some examples, D2D connections may be made using licensed spectrumbands, and such connections may be managed by a cellular network orservice provider. Accordingly, while the above example was described inthe context of a narrowband IoT, it can be appreciated that otherdevice-to-device connections may be utilized by virtual reality device850.

In various examples, the elements of wireless communications system 800,such as the mobile device 815, the drone 817, the communication device820, the small cell 830, the networked workstations 840, 845, thevirtual reality device 850, the IoT devices 855, 860, and the networkedentertainment device 865, may be implemented as part of any exampledescribed herein, such as electronic device 102, 110 of FIG. 2,electronic device 110 of FIG. 5, or any system or combination of thesystems depicted in the Figures described herein.

FIG. 9 is a block diagram of an electronic device 900 arranged inaccordance with examples described herein. The electronic device 900 mayoperate in accordance with any example described herein, such aselectronic device 102, 110 of FIG. 2, electronic device 110 of FIG. 5,or any system or combination of the systems depicted in the Figuresdescribed herein. The electronic device 900 may be implemented in asmartphone, a wearable electronic device, a server, a computer, anappliance, a vehicle, or any type of electronic device. The electronicdevice 900 includes a computing system 902, a neuron calculator 940, anI/O interface 970, and a network interface 990 coupled to a network 995.The computing system 902 includes a wireless transceiver 910. Thewireless transceiver may include a wireless transmitter and/or wirelessreceiver, such as wireless transmitter 300 and wireless receiver 400.Neuron calculator 940 may include any type of microprocessor, centralprocessing unit (CPU), an application specific integrated circuits(ASIC), a digital signal processor (DSP) implemented as part of afield-programmable gate array (FPGA), a system-on-chip (SoC), or otherhardware to provide processing for device 900.

The computing system 902 includes memory 950 (e.g., memory look-upunit), which may be non-transitory hardware readable medium includinginstructions, respectively, for calculating neuron or be memory for theretrieval, calculation, or storage of data signals to be compensated oradjusted signals based on calculated neuron. The neuron calculator 940may control the computing system 902 with control instructions thatindicate when to execute such stored instructions for calculating neuronor for the retrieval or storage of data signals to be compensated oradjusted signals based on calculated neuron. Upon receiving such controlinstructions, the wireless transceiver 910 may execute suchinstructions. For example, such instructions may include a program thatexecutes the method 600. Communications between the neuron calculator940, the I/O interface 970, and the network interface 990 are providedvia an internal bus 980. The neuron calculator 940 may receive controlinstructions from the I/O interface 970 or the network interface 990,such as instructions to calculate ordered sets for ordered neurons orconnection weights.

Bus 980 may include one or more physical buses, communicationlines/interfaces, and/or point-to-point connections, such as PeripheralComponent Interconnect (PCI) bus, a Gen-Z switch, a CCIX interface, orthe like. The I/O interface 970 can include various user interfacesincluding video and/or audio interfaces for the user, such as a tabletdisplay with a microphone. Network interface 990 communications withother electronic devices, such as electronic device 900 or acloud-electronic server, over the network 995. For example, the networkinterface 990 may be a USB interface.

Certain details are set forth above to provide a sufficientunderstanding of described examples. However, it will be clear to oneskilled in the art that examples may be practiced without various ofthese particular details. The description herein, in connection with theappended drawings, describes example configurations and does notrepresent all the examples that may be implemented or that are withinthe scope of the claims. The terms “exemplary” and “example” as may beused herein means “serving as an example, instance, or illustration,”and not “preferred” or “advantageous over other examples.” The detaileddescription includes specific details for the purpose of providing anunderstanding of the described techniques. These techniques, however,may be practiced without these specific details. In some instances,well-known structures and devices are shown in block diagram form inorder to avoid obscuring the concepts of the described examples.

Information and signals described herein may be represented using any ofa variety of different technologies and techniques. For example, data,instructions, commands, information, signals, bits, symbols, and chipsthat may be referenced throughout the above description may berepresented by voltages, currents, electromagnetic waves, magneticfields or particles, optical fields or particles, or any combinationthereof.

Techniques described herein may be used for various wirelesscommunications systems, which may include multiple access cellularcommunication systems, and which may employ code division multipleaccess (CDMA), time division multiple access (TDMA), frequency divisionmultiple access (FDMA), orthogonal frequency division multiple access(OFDMA), or single carrier frequency division multiple access (SC-FDMA),or any a combination of such techniques. Some of these techniques havebeen adopted in or relate to standardized wireless communicationprotocols by organizations such as Third Generation Partnership Project(3GPP), Third Generation Partnership Project 2 (3GPP2) and IEEE. Thesewireless standards include Ultra Mobile Broadband (UMB), UniversalMobile Telecommunications System (UMTS), Long Term Evolution (LTE),LTE-Advanced (LTE-A), LTE-A Pro, New Radio (NR), IEEE 802.11 (WiFi), andIEEE 802.16 (WiMAX), among others.

The terms “5G” or “5G communications system” may refer to systems thatoperate according to standardized protocols developed or discussedafter, for example, LTE Releases 13 or 14 or WiMAX 802.16e-2005 by theirrespective sponsoring organizations. The features described herein maybe employed in systems configured according to other generations ofwireless communication systems, including those configured according tothe standards described above.

The various illustrative blocks and modules described in connection withthe disclosure herein may be implemented or performed with ageneral-purpose processor, a digital signal processor (DSP), anapplication-specific integrated circuit (ASIC), a field-programmablegate array (FPGA), or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions described herein. Ageneral-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices (e.g., a combinationof a DSP and a microprocessor, multiple microprocessors, one or moremicroprocessors in conjunction with a DSP core, or any other suchconfiguration).

The functions described herein may be implemented in hardware, softwareexecuted by a processor, firmware, or any combination thereof. Ifimplemented in software executed by a processor, the functions may bestored on or transmitted over as one or more instructions or code on acomputer-readable medium. Computer-readable media includes bothnon-transitory computer storage media and communication media includingany medium that facilitates transfer of a computer program from oneplace to another. A non-transitory storage medium may be any availablemedium that can be accessed by a general purpose or special purposecomputer. By way of example, and not limitation, non-transitorycomputer-readable media can comprise RAM, ROM, electrically erasableprogrammable read only memory (EEPROM), or optical disk storage,magnetic disk storage or other magnetic storage devices, or any othernon-transitory medium that can be used to carry or store desired programcode means in the form of instructions or data structures and that canbe accessed by a general-purpose or special-purpose computer, or ageneral-purpose or special-purpose processor.

Also, any connection is properly termed a computer-readable medium. Forexample, if the software is transmitted from a website, server, or otherremote source using a coaxial cable, fiber optic cable, twisted pair,digital subscriber line (DSL), or wireless technologies such asinfrared, radio, and microwave, then the coaxial cable, fiber opticcable, twisted pair, DSL, or wireless technologies such as infrared,radio, and microwave are included in the definition of medium.Combinations of the above are also included within the scope ofcomputer-readable media.

Other examples and implementations are within the scope of thedisclosure and appended claims. For example, due to the nature ofsoftware, functions described above can be implemented using softwareexecuted by a processor, hardware, firmware, hardwiring, or combinationsof any of these. Features implementing functions may also be physicallylocated at various positions, including being distributed such thatportions of functions are implemented at different physical locations.

Certain details are set forth herein to provide a sufficientunderstanding of embodiments of the present disclosure. However, it willbe clear to one skilled in the art that embodiments of the presentdisclosure may be practiced without various of these particular details.In some instances, well-known wireless communication components,circuits, control signals, timing protocols, computing systemcomponents, telecommunication components, and software operations havenot been shown in detail in order to avoid unnecessarily obscuring thedescribed embodiments of the present disclosure.

Also, as used herein, including in the claims, “or” as used in a list ofitems (for example, a list of items prefaced by a phrase such as “atleast one of” or “one or more of”) indicates an inclusive list suchthat, for example, a list of at least one of A, B, or C means A or B orC or AB or AC or BC or ABC (i.e., A and B and C). Also, as used herein,the phrase “based on” shall not be construed as a reference to a closedset of conditions. For example, an exemplary step that is described as“based on condition A” may be based on both a condition A and acondition B without departing from the scope of the present disclosure.In other words, as used herein, the phrase “based on” shall be construedin the same manner as the phrase “based at least in part on.”

From the foregoing it will be appreciated that, although specificexamples have been described herein for purposes of illustration,various modifications may be made while remaining with the scope of theclaimed technology. The description herein is provided to enable aperson skilled in the art to make or use the disclosure. Variousmodifications to the disclosure will be readily apparent to thoseskilled in the art, and the generic principles defined herein may beapplied to other variations without departing from the scope of thedisclosure. Thus, the disclosure is not limited to the examples anddesigns described herein, but is to be accorded the broadest scopeconsistent with the principles and novel features disclosed herein.

What is claimed is:
 1. A method comprising: receiving a plurality ofcalibration signals; generating a second-order set for a plurality ofordered sets based at least in part on multiplying each calibrationsignal of the plurality with another calibration signal of the pluralityof calibration signals; allocating the second-order set to asecond-order neuron of a neuron calculator; and calculating a pluralityof signals at the neuron calculator with the second-ordered neuronwherein calculating the plurality of signals at the neuron calculatorcomprises: combining, at at least a portion of a plurality ofmultiplication/accumulation processing units of the second-orderedneuron, first and second signals of the plurality of signals with thesecond-order set to generate a plurality of intermediate signals; andcombining, at at least another portion of a plurality ofmultiplication/accumulation processing units of the second-orderedneuron, the plurality of intermediate signals with the second-order setto generate a plurality of output signals.
 2. A method comprising:receiving a plurality of calibration signals; generating a second-orderset for a plurality of ordered sets based at least in part onmultiplying each calibration signal of the plurality with anothercalibration signal of the plurality of calibration signals, whereingenerating the second-order set comprises: multiplying a firstcalibration signal of the plurality with the first calibration signal togenerate a first multiplicative processing result of the second-orderset; multiplying the first calibration signal with the other calibrationsignal of the plurality to generate a second multiplicative processingresult of the second-order set; multiplying the other calibration signalwith the first calibration signal to generate a third multiplicativeprocessing result of the second-order set; and multiplying the othercalibration signal with the other calibration signal to generate afourth multiplicative processing result of the second-order set;allocating the second-order set to a second-order neuron of a neuroncalculator; and processing signals at the neuron calculator with thesecond-ordered neuron.
 3. The method of claim 1, further comprising:generating a plurality of connection weights for a correspondingconnection between each of a first-order neuron and the second-orderneuron of the neuron calculator and a respective output of a pluralityof outputs of the neuron calculator.
 4. The method of claim 3, whereinthe first-ordered neuron comprises each calibration signal of theplurality of calibration signals as the first-order set.
 5. The methodof claim 4, further comprising: combining, at each output of the neuroncalculator, the first-order set and the second-order set with at least aportion of the connection weights to generate compensated calibrationsignals.
 6. The method of claim 4, wherein generating the plurality ofconnection weights for the corresponding connection comprises: randomlyselecting the plurality of connection weights; reducing an error ofcompensated calibrations signals based on a summation of the pluralityof connection weights and the first-order set and the second-order set.7. The method of claim 4, further comprising providing, to the neuroncalculator, a first radio frequency (RF) signal associated with a firstfrequency as the first signal of the plurality of signals and a secondRF signal associated with a second frequency as the second signal of theplurality of signals, wherein the first RF signal is received at a firstantenna of a plurality of antennas and the second RE signal is receivedat a second antenna of the plurality of antennas; mixing the first andsecond RF signals in accordance with the first-order set or second-orderset and the plurality of connection weights to generate the plurality ofoutput signals, the plurality of output signals having a reduced errorrelative to the first and second RF signals.
 8. The method of claim 7,wherein a quantity of the plurality of antennas corresponds to a numberof antennas of a MIMO antenna array.
 9. The method of claim 7, whereinfirst antenna of the plurality of antennas is configured to receive at aradio frequency associated with a 5G wireless protocol.
 10. A methodcomprising: generating a kth-order set for a plurality of ordered setsbased at least in part on multiplying each calibration signal of aplurality of calibration signals with at least another calibrationsignal of the plurality of calibration signals, wherein k represents anumber of the plurality of calibration signals that are selected;allocating the kth-order set to a kth-ordered neuron of a neuralnetwork; and calculating a plurality of signals at the neural networkwith the kth-ordered neuron, wherein calculating the plurality ofsignals at the neuron neural network with the kth-ordered neuroncomprises: combining, at at least a portion of a plurality ofmultiplication/accumulation processing units of the kth-ordered neuron,a plurality of signals with the kth-order set to generate a plurality ofintermediate signals; and combining, at at least another portion of aplurality of multiplication/accumulation processing units of thekth-ordered neuron, the plurality of intermediate signals with thekth-ordered set to generate a plurality of output signals.
 11. Themethod of claim 10, wherein the kth-order set comprises product valuesbased on combinations of at least one calibration signal and anothercalibration signal multiplied with itself k-l times, wherein lcorresponds to each output of each neuron.
 12. The method of claim 10,wherein generating a kth-order set for a plurality of ordered setscomprising selecting a set of k-combinations including repetition fromamong the plurality of calibration signals.
 13. The method of claim 10,wherein calculating the plurality of signals at the neuron neuralnetwork with the kth-ordered neuron comprises: obtaining a plurality ofradio frequency (RF) signals from a respective antenna of a plurality ofantennas; and mixing, at the kth-ordered neuron, the kth-order set andconnection weights with the plurality of RF signals as the plurality ofsignals to generate the plurality of output signals.
 14. The method ofclaim 10, wherein allocating the kth-order set to a kth-ordered neuronof a neural network comprises determining that, the kth-order set is tobe allocated to one or more processing units, at the kth-ordered neuron.15. The method of claim 10, wherein at least one processing unit of theone or more processing units comprises the plurality ofmultiplication/accumulation processing units configured to multiply andaccumulate signals and a plurality of memory look-up units configured tostore the kth-order set.
 16. An apparatus comprising: a first receiverconfigured to process a first radio frequency (RF) signal; a secondreceiver configured to process a second RF signal; and a processing unitcoupled to the first receiver and the second receiver and configured toreceive a first input signal based on the first RF signal and a secondinput signal based on the second RF signal, the processing unitconfigured to calculate a plurality of ordered sets and a plurality ofconnection weights to generate a plurality of output signals, whereinthe processing unit comprises a plurality of multiplication/accumulationprocessing units and a plurality of memory look-up units, wherein theprocessing unit further comprises a non-transitory computer readablemedia encoded with executable instructions which, when executed by theat least one processing unit, is configured to cause the apparatus toperform operations comprising: combining, at at least a portion of theplurality of multiplication/accumulation processing units, the first andsecond input signals with the plurality of ordered sets to generate aplurality of intermediate signals; and combining, at at least anotherportion of the plurality of multiplication/accumulation processingunits, the plurality of intermediate signals with the plurality ofordered sets to generate the plurality of output signals.
 17. Theapparatus of claim 16, wherein the processing unit is configured toperform a channel estimation of the first and second input signals andto provide the plurality of output signals as compensated symbols. 18.The apparatus of claim 16, wherein the operations further comprising:obtaining, from at least a portion of the plurality of memory look-upunits, the plurality of ordered sets.